Using interval arithmetic to prove that a set is path-connected

Abstract: In this paper, we give a numerical algorithm able to prove whether a set described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as . Examples illustrate the principle of the approach. [Copyright &y& Elsevier]